Most simply stated, a laser comprises an energizeable lasing medium confined in an optical resonator cavity. Typically, the laser comprises a tube for containing the lasing medium with mirrors at each longitudinal end defining the resonator cavity. The frequency of the output is determined by the properties of the lasing medium and the configuration of the resonator.
Considering the lasing medium, the central frequency of the output is determined by the available laser transitions of the medium. The transition promoted in most helium-neon lasers results in an output having a wavelength of 6328 angstroms. Due to the thermal motion along the lasing axis of the atoms that comprise the lasing medium, output frequencies shifted up or down from the central frequency are possible. The intensity distribution of the shifted output frequencies is defined by a curve usually referred to as the Doppler profile. It is often predicted by the following equation: EQU I=I.sub.o (exp (-Mc.sup.2 .DELTA.v.sup.2 /2v.sub.o.sup.2 KT)-1).eta..sup.2
where
v.sub.o is the unshifted or central frequency, PA1 I.sub.o is the intensity at the central frequency, PA1 .eta. is the ratio of available centerline gain to total losses (i.e. g.sub.o /total losses), PA1 M is atomic mass, PA1 c is the speed of light, PA1 KT is an electron temperature relationship, and PA1 .DELTA.v is the difference frequency of a given mode from the centerline.
FIG. 1(a) illustrates a typical Doppler profile, that is, the frequency spectrum versus gain relation for a hypothetical lasing medium with a central lasing frequency of v.sub.o and an intensity at that frequency of I.sub.o. The gain at frequencies on both sides of the central frequency drop off until falling below the loss threshold. The immediate significance of the Doppler profile (or the effect it quantifies known as Doppler broadening) is that a laser can potentially output light over a range of frequencies near the central frequency. However, as the gain of a Doppler shifted frequency falls below a loss threshold, resonances cannot be sustained.
Considering now the optical resonator cavity, the end mirrors of the cavity define the length of the cavity along the optical axis. For any cavity there exists normal modes or field configurations that will sustain oscillations within the resonator. The modes of a laser resonator are typically defined by the symbol TEMmnq where m, n, and q define the number of modes, n, m in the transverse directions and q the number of modes in the longitudinal direction. For helium-neon lasers the numbers m, n are usually very small and often zero. The number q defines the number of longitudinal modes (the number of half wavelengths between the two mirrors) and is usually a very large number. The number q also defines the number of longitudinal modes for a given cavity. For any given cavity length, L in centimeters, the frequency spacing of the available modes will be C/2L in Megahertz. Hence, the shorter the length L, the further apart the frequencies that will resonate within a given optical cavity. FIG. 1(b) illustrates the frequency spectrum of an optical resonator cavity of length L for the TEMOOq modes.
The interaction between the available cavity modes and the frequencies which the lasing medium will support under its Doppler profile are illustrated by FIG. 1(c) which is the intersection of FIGS. 1(a) and 1(b). For the hypothetical laser described there exists three modes under the Doppler profile and three frequencies that will be emitted by the laser. If the spacing C/2L is large enough, only a single frequency will be emitted.
In a helium-neon laser, as with the hypothetical laser already described, only those resonances which have sufficient gain will oscillate. This gain is available from the population inversion between the valence states 3s.sub.2 and 2p.sub.4 for the 6328 angstrom line in neon. In most helium-neon lasers, natural neon is used which is comprised of a mixture of the isotopes of Ne.sub.22 and Ne.sub.20 with about 80% being the latter.
In order to obtain a more uniform gain profile, a single isotope fill is utilized in most cases using Ne.sub.20. Also, by choosing a single isotope of neon, a well defined centerline frequency can be used as a frame of reference.
Power output of the laser will vary by changes in the mode location under the Doppler gain profile. This change is often referred to as "mode-sweeping". Since mode location is influenced by the mode spacing C/2L, changes in cavity length will cause frequency shifting through the gain profile and thus cyclic changes in output power. By controlling the cavity spacing, one is able to control the desired output power or output frequency.
Mode sweeping can be described quite easily. Note that small changes to the cavity length resulting, say, due to temperature changes, will result in a small change to the mode spacing as described. While these changes are barely noticeable in the low frequency portion of the spectrum, their effect is cumulative in nature and will be quite noticeable in the frequency region of v.sub.o (the region of laser output).
As temperature increases, the cavity will expand causing the mode spacing C/2L to decrease. This will have the effect on the modes in the vicinity of v.sub.o to shift towards the low frequency domain. The opposite is true for temperature decreases. It is this phenomena which allows for the control of linear output single frequency lasers.
The approaches used to expand and contract the cavity may vary. Heating the cavity is widely used since it is easy to generate and control. However, response can be quite slow especially for designs with large thermal inertias. Piezoelectric crystals have also been employed which are generally much more responsive bu suffer due to the fact that they are more difficult and expensive to apply.
The output powers associated with the cavity modes that oscillate under the Doppler profile each have a distinct frequency. Obviously for very short lasers the mode spacing will be larger and only one mode would be able to fit under the gain profile at one time. This would correspond to a cavity length of less than 4.5 inches. For very long lasers, many cavity modes may oscillate at one time. For instance, a known 16 mW helium-neon laser (over 30 inches long) can oscillate with up to 13 modes if the cavity losses are sufficiently small.
The laser length that is popular in most stabilized frequency applications is about 7 to 9 inches. At this length no more than 2 modes can oscillate at one time (which is important) and over lmW can be generated by a single mode.
Each mode under the profile is not only distinct from adjacent modes by its frequency but also by its polarization. For instance, in a laser oscillating in two modes, the polarization of each mode will be orthogonal to the adjacent mode (angularly spaced by 90.degree.). Such modes are often referred to as being "s" and "p" polarized With the addition of each mode the polarization will alternate as "s", "p", "s", etc. This fact is why no more than three modes can be tolerated for a single frequency laser application. A polarizer, for example, would pass two modes and coherence would be lost.
The term "randomly polarized" to describe lasers without Brewster windows is somewhat misleading. In fact, there is nothing "random" about such a tube. As described earlier, each mode as it enters the profile during mode sweeping takes on a polarization orthogonal to the adjacent mode. However, the orientation of the "s" or "p" cavity modes with respect to the laser tube does not move appreciably during the life of the tube. They become locked to a position on the tube caused by conditions during manufacturing. The phenomena that causes this polarization sensitivity is known as birefringence.
It is known that a certain level of birefringence is required for a "random" laser tube to be used in a single frequency application. Without it, the polarizations would migrate "randomly". However, too much stress birefringence can cause a phenomena known as "mode hopping". In this case, polarization sensitivity is more strongly oriented to either the "s" or "p" polarization plane so that as the intensity of the "unfavored" mode grows (and the intensity of the "favored" mode decreases), it hops to the favored polarization. This phenomena is unwanted in single frequency applications.
Most single frequency lasers, no matter the serv.sub.o technique, use a signal indicative of power associated with the individual modes as the feedback signal. The exceptions are iodine stabilized lasers and Zeemen Split Lasers, in which the latter required the use of a quarter wave plate to produce linear output. Therefore, most single frequency lasers are power stabilized lasers. Most manufacturers specify the level of frequency stability in terms of MHz or parts per billion.
As stated, power stabilization can be effected by adjusting the length of the laser cavity, that is, the length between the mirrors at each end. Thermal expansion has been used to adjust the length of prior helium-neon lasers. It is a desired method since standard tube designs can be employed. In these systems all or a portion of the laser cavity is heated by radiation or convection. However, use of thermal expansion and radiation or convection heating has a drawback; namely, a relatively long time constants within the control loop. A less used prior system is based upon piezoelectric control of the cavity length. In that system, a voltage sensitive crystal is used to vary the cavity length and thus provide much more rapid response but requires especially constructed laser tubes.